Modeling Anomalous Diffusion and Dual-Porosity Behavior in Fractured Reservoirs Using Fractional Calculus

This paper presents a novel approach for modeling fluid transport mechanisms within highly heterogeneous and fractured porous media by leveraging the structural advantages of fractional calculus. Traditional hydro-dynamic frameworks often fail to capture the intrinsic memory effects and anomalous diffusion commonly observed during pressure transients in complex oil wells. To overcome these limitations, we formulate a generalized mathematical model governed by spatial-temporal fractional partial differential equations. By substituting classical derivatives with non-local operators, our framework successfully replicates the sub-diffusive behavior induced by reservoir anisotropy and complex fracture networks. The analytical solutions demonstrate that fractional-order parameters provide a more robust and accurate representation of pressure decline over time, establishing a precise predictive tool for optimizing flow equations and production diagnostics in non-conventional petroleum engineering.